Susan wants to make aprons for cooking. She needs one and three fourths yards of fabric for the front of the apron and three eighths yards of fabric for the tie.
Part A: Calculate how much fabric is needed to make 3 aprons? Show every step of your work. (5 points)
Part B: If Susan originally has 7 yards of fabric, how much is left over after making the aprons? Show every step of your work. (5 points)
Part C: Does Susan have enough fabric left to make another apron? Explain why or why not. (2 points)
Part A:
To make 3 aprons, Susan will need:
3 * (1 3/4) = 5 1/4 yards of fabric for the front of the apron
3 * (3/8) = 9/8 = 1 1/8 yards of fabric for the tie
Therefore, Susan will need a total of 5 1/4 + 1 1/8 = 6 3/8 yards of fabric to make 3 aprons.
Part B:
If Susan starts with 7 yards of fabric and uses 6 3/8 yards to make the aprons, she will have:
7 - 6 3/8 = 7 - (6 + 3/8) = 7 - (5 + 1/8) = 7 - 5 - 1/8 = 2 - 1/8 = 1 7/8 yards of fabric left.
Part C:
Susan does not have enough fabric left to make another apron, as she would need 1 3/4 yards of fabric for the front and 3/8 yards for the tie, which totals to 2 1/8 yards of fabric. Since Susan only has 1 7/8 yards remaining, she does not have enough fabric to make another apron.
Part A:
To make 3 aprons, Susan will need:
3 * (1 3/4) = 5 1/4 yards of fabric for the front of the apron
3 * (3/8) = 9/8 = 1 1/8 yards of fabric for the tie
Therefore, Susan will need a total of 5 1/4 + 1 1/8 = 6 3/8 yards of fabric to make 3 aprons.
Part B:
If Susan starts with 7 yards of fabric and uses 6 3/8 yards to make the aprons, she will have:
7 - 6 3/8 = 7 - (6 + 3/8) = 7 - (5 + 1/8) = 7 - 5 - 1/8 = 2 - 1/8 = 1 7/8 yards of fabric left.
Part C:
Susan does not have enough fabric left to make another apron, as she would need 1 3/4 yards of fabric for the front and 3/8 yards for the tie, which totals to 2 1/8 yards of fabric. Since Susan only has 1 7/8 yards remaining, she does not have enough fabric to make another apron.
Part A:
To make 3 aprons, Susan will need:
3 * (1 3/4) = 5 1/4 yards of fabric for the front of the apron
3 * (3/8) = 9/8 = 1 1/8 yards of fabric for the tie
Therefore, Susan will need a total of 5 1/4 + 1 1/8 = 6 3/8 yards of fabric to make 3 aprons.
Part B:
If Susan starts with 7 yards of fabric and uses 6 3/8 yards to make the aprons, she will have:
7 - 6 3/8 = 7 - (6 + 3/8) = 7 - (5 + 1/8) = 7 - 5 - 1/8 = 2 - 1/8 = 1 7/8 yards of fabric left.
Part C:
Susan does not have enough fabric left to make another apron, as she would need 1 3/4 yards of fabric for the front and 3/8 yards for the tie, which totals to 2 1/8 yards of fabric. Since Susan only has 1 7/8 yards remaining, she does not have enough fabric to make another apron.
Part A: To calculate how much fabric is needed to make 3 aprons, we need to add up the fabric needed for the front and the tie.
Fabric for the front:
One and three fourths yards of fabric are needed for each apron.
So, for 3 aprons, we multiply 1 and 3/4 by 3:
1 and 3/4 * 3 = (4/4 + 3/4) * 3 = 7/4 * 3 = 21/4 = 5 and 1/4 yards.
Fabric for the tie:
Three-eighths of a yard of fabric is needed for each apron.
So, for 3 aprons, we multiply 3/8 by 3:
3/8 * 3 = 9/8 = 1 and 1/8 yards.
Total fabric needed for 3 aprons:
Front fabric: 5 and 1/4 yards
Tie fabric: 1 and 1/8 yards
Total = 5 and 1/4 + 1 and 1/8 = (21/4) + (9/8) = (42/8) + (9/8) = 51/8 = 6 and 3/8 yards.
Therefore, 6 and 3/8 yards of fabric are needed to make 3 aprons.
Part B: To calculate how much fabric is left over after making the aprons, we subtract the total fabric needed from the original amount of fabric.
Original amount of fabric: 7 yards
Fabric used for aprons: 6 and 3/8 yards
To subtract the fractional value, we convert it to a common denominator of 8:
6 and 3/8 = 48/8 + 3/8 = 51/8 yards.
Fabric left over: 7 - (51/8) = 8/1 - (51/8) = (64/8) - (51/8) = 13/8 = 1 and 5/8 yards.
Therefore, 1 and 5/8 yards of fabric are left over after making the aprons.
Part C: Susan does not have enough fabric left to make another apron because she only has 1 and 5/8 yards of fabric left, but she needs 6 and 3/8 yards to make one apron. Therefore, she does not have enough fabric to make another apron.
Part A:
To calculate how much fabric is needed to make 3 aprons, we need to add up the fabric needed for the front and the tie for each apron.
Fabric needed for the front of one apron = 1 and 3/4 yards.
Fabric needed for the tie of one apron = 3/8 yards.
Now, let's calculate the total fabric needed for 3 aprons:
Fabric needed for the front of 3 aprons = (1 and 3/4 yards) * 3 = (7/4 yards) * 3 = 21/4 yards.
Fabric needed for the tie of 3 aprons = (3/8 yards) * 3 = 9/8 yards.
Total fabric needed for 3 aprons = Fabric needed for the front + Fabric needed for the tie
= 21/4 yards + 9/8 yards.
To add these fractions, we need to find a common denominator.
The least common denominator (LCD) of 4 and 8 is 8.
Converting the fractions to have a common denominator of 8:
Fabric needed for the front of 3 aprons = (21/4 yards) * (2/2) = 42/8 yards.
Fabric needed for the tie of 3 aprons = (9/8 yards) * (1/1) = 9/8 yards.
Adding the fractions:
Total fabric needed for 3 aprons = 42/8 yards + 9/8 yards = (42 + 9) / 8 = 51/8 yards.
Therefore, to make 3 aprons, Susan needs a total of 51/8 yards of fabric.
Part B:
To calculate how much fabric is left over after making the aprons, we need to subtract the fabric used for the aprons from the initial amount of fabric.
Initial amount of fabric = 7 yards.
Total fabric used for 3 aprons = 51/8 yards (calculated in Part A).
Fabric left over = (Initial amount of fabric) - (Total fabric used for 3 aprons)
= 7 yards - 51/8 yards.
To subtract fractions with different denominators, we need to find a common denominator.
The common denominator of 1 and 8 is 8.
Converting the fractions to have a common denominator of 8:
Fabric left over = (7 yards) * (8/8) - (51/8 yards) = 56/8 yards - 51/8 yards.
Subtracting the fractions:
Fabric left over = (56 - 51) / 8 = 5/8 yards.
Therefore, after making the aprons, Susan has 5/8 yards of fabric left over.
Part C:
Susan has 5/8 yards of fabric left over.
To determine if she has enough fabric to make another apron, we need to compare the amount of fabric left with the fabric needed for one apron.
Fabric needed for one apron (front + tie) = 1 and 3/4 yards + 3/8 yards.
Adding the fractions:
Fabric needed for one apron = (7/4 yards) + (3/8 yards).
To add these fractions, we need to find a common denominator.
The least common denominator (LCD) of 4 and 8 is 8.
Converting the fractions to have a common denominator of 8:
Fabric needed for one apron = (7/4 yards) * (2/2) + (3/8 yards) * (1/1)
= 14/8 yards + 3/8 yards.
Adding the fractions:
Fabric needed for one apron = (14 + 3) / 8 = 17/8 yards.
Since Susan has 5/8 yards of fabric left over, which is less than the 17/8 yards needed for one apron, she does not have enough fabric left to make another apron.